There have been developments since that post, but I thank you for your thoughts.
The roofer has been back a couple of times and found that around eight of the concrete tiles are cracked, he lifted the tiles and found that the batons underneath were rotten and that the lining was only made for a couple of years in the 1990s and withdrawn, mainly because it didn't breathe and caused condensation problems. The damaged tiles have been replaced, the batons cut back to good wood and replaced, the lining has been replaced, as needed.
I did think about why so many tiles would be broken, given that no one has walked on them, I am presuming that the rotten batons allowed the tiles to move and perhaps lift causing stress cracks.
We are planning on a completely new roof with better tiles and lining and thicker batons come spring and the drier weather.
The damp patch has now gone although I am waiting for a downpour to be certain.